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arXiv · 1312.5504

Metastability for parabolic equations with drift: part 1

Hitoshi Ishii·Panagiotis E. Souganidis
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Abstract

We provide a self-contained analysis, based entirely on pde methods, of the exponentially long time behavior of solutions to linear uniformly parabolic equations which are small perturbations of a transport equation with vector field having a globally stable point. We show that the solutions converge to a constant, which is either the initial value at the stable point or the boundary value at the minimum of the associated quasi-potential. This work extends previous results of Freidlin and Wentzell and Freidlin and Koralov and applies also to semilinear elliptic pde.

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Hitoshi Ishii, Panagiotis E. Souganidis. 2013-12-19. Metastability for parabolic equations with drift: part 1. https://doi.org/10.1512/iumj.2015.64.5559

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